1. Field of the Invention
The present invention relates to a method of and an arrangement for determining the optimum position of the reference tap of an adaptive equalizer which adapts itself to variations of the channel of a digital transmission system, and more specifically for high-rate systems in which the transmission channel is not known in advance and/or is liable to vary in the course of time. Consequently, the invention is applicable to digital microwave links, to data transmission via switched telephone networks, to the digital transmission via cables (special networks of the Transpac type, etc . . . ).
2. Description of the Related Art
Multiple-path selective fading seriously affects the capacity of digital radio transmission systems. Similarly, the transmission of data via cables often results in distortion and intersymbol interference. Thus, to combat the disturbances appearing in the dispersive channels, it is necessary to perform adaptation procedures which render it possible to recover the transmitted data on receipt. However so as to follow adequately the fluctuations of the channel it is necessary that these adaptation procedures are effected automatically.
The adaptive equalizers arranged at the receiving end of the digital transmission systems ensure the regeneration of the symbols transmitted by the transmitter by determining the estimated symbols on the basis of adaptation and decision criteria.
Generally, the data x.sub.k obtained from the transmission channel are assumed to be complex data, which renders it necessary that the adaptive equalizers under consideration process simultaneously the real and imaginary components of said complex data. It will be evident that in the case of purely real data x.sub.k will be obtained as a direct result of such processing.
Conventionally, the adaptive equalizers are of two types:
either a non-recursive transversal filter in which N delayed samples, originating from the complex data x.sub.k, are multiplied by N complex coefficients, the N results thus obtained being added together to define the received signal;
or a recursive transversal filter in which, in addition to a non-recursive transversal filter of the above type, there is a recursive branch, that is to say a branch which reintroduces in the equalizer, M complex data appearing at the output of the equalizer, these M data being multiplied respectively by M complex coefficients, thereafter added to the N data of the non-recursive branch, the recursive loop comprising inter alia a nonlinear decision element.
The adaptation is effected on the basis of an error criterion and an algorithm which minimizes this error criterion.
It is also known that in certain circumstances it may be useful to have the adaptive equalizer be preceded by a filter which is matched to the impulse response of the channel. Nevertheless, in practice the impulse response of the channel is generally not known in advance and so use of a matched filter is not the best solution. When the adaptive equalizer is not preceded by a matched filter, the centre tap of the equalizer has been used as the reference tap. However, a better solution is to provide an adaptive selection procedure for the optimum position of the reference tap.
For a correct adaptation to the variations of the channel two adaptation procedures may be performed simultaneously:
a procedure for adapting the N+M coefficients;
a procedure for adapting the position of the reference tap, this position defining the delay of the adaptive equalizer and its performances.
The adaptation algorithm utilized for the N+M coefficients is, for example, a mean-square error stochastic gradient-type algorithm.
An arrangement for adjusting the position of the reference tap in an adaptive equalizer is described by SHAHID U. H. QURESHI in the article entitled "Adjustment of the Position of the Reference Tap of an Adaptive Equalizer", published in IEEE Transactions on Communications, Vol COM. 21, No. 9, pages 1046-1052, September 1973. That arrangement uses the known method of stochastic adjustment of the gradient of the mean-square error to determine the optimum position of the reference tap. Unfortunately, as is explained in said article, the convergence of this method to a global minimum cannot be guaranteed. In other words, the method may converge to an intermediate minimum, which does not correspond to the feasible optimum adaptation. There is consequently a risk of an imperfect adaptation, which diminishes the reliability of this method. On the other hand, even in the most advantageous case in which a convergence to a global minimum is obtained, the adaptation procedure causes fluctuations of the position of the reference tap around the point of equilibrium.